In recent years, the petroleum industry has invested heavily in the development of improved marine survey techniques and seismic data processing methods in order to increase the resolution and accuracy of seismic images of subterranean formations. Marine surveys illuminate a subterranean formation located beneath a body of water with acoustic signals produced by one or more submerged sources. A source may be composed of an array of source elements, such as air guns or marine vibrators. The acoustic signals travel down through the water and into the subterranean formation. At interfaces between different types of rock or sediment of the subterranean formation, a portion of the acoustic signal energy may be refracted, a portion may be transmitted, and a portion may be reflected back toward the formation surface and into the body of water. A typical marine survey is carried out with a survey vessel that passes over the illuminated subterranean formation while towing elongated cable-like structures called streamers. The streamers may be equipped with a number of receivers for detecting and/or measuring seismic energy. Often, the receivers may be collocated pressure and particle motion sensors that detect pressure and particle motion wavefields, respectively, associated with the acoustic signals reflected back into the water from the subterranean formation. The pressure sensors may generate seismic data that represents the pressure wavefield (“pressure data”), and the particle motion sensors may generate seismic data that represents the particle motion, particle velocity, or particle acceleration wavefield (“particle motion data”). Equipment on the survey vessel may receive and record the seismic data generated by the receivers.
A wavefield that travels upward from the subterranean formation and is detected by the pressure or particle motion sensors is called an up-going wavefield, which alone may be used to compute a seismic image of the subterranean formation. However, the surface of the water acts as a nearly perfect acoustic reflector. As a result, the receivers also detect a down-going wavefield created by reflection of the up-going wavefield from the water surface. The down-going wavefield is essentially the up-going wavefield with a time delay that corresponds to the amount of time it takes for acoustic signals to travel up past the streamers to the water surface and back down to the streamers. The down-going wavefield combines with the up-going wavefield, resulting in recorded seismic data contaminated with unwanted down-going wavefield energy that creates “ghost” effects in seismic images of the subterranean formation computed from the seismic data. Wavefield separation techniques compute the up-going wavefield based on pressure and particle motion wavefields.